Session D1: Fluctuation and Relaxation Near Jamming

Dynamic model of super-Arrhenius relaxation rates in glassy materials

The principal theme of this talk is that anomalously slow, super- Arrhenius relaxation processes in glassy materials may be activated by chains of atomic displacements. The entropy of critically long excitation chains can enable them to grow without bound, thus stabilizing thermal fluctuations in the local density or atomic coordination of the material. I argue that the intrinsic atomic-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that the resulting rate formula is essentially the same as the Vogel-Fulcher law. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that ergodicity is partially broken in the super-Arrhenius region above that temperature, and point out how this partially broken ergodicity may explain the vanishing entropy at that point and other observed relations between dynamics and thermodynamics of the glass transition.   

Experimental studies of jamming in colloids, grains and emulsions

We review experimental progress towards the development of a statistical mechanics description of jamming in colloids, granular matter and emulsions. The approach is to consider the application of equilibrium concepts such as temperature, entropy and thermalization to this variety of jammed systems. We first present a study of the correlation and response functions to external fields in an aging colloidal glass. Our analysis reveals that even though the system is aging far from equilibrium, it behaves as if it were equilibrated at a constant temperature, independent of its age. This temperature is larger than the bath, and can be rationalized by the cage dynamics of the system and also in terms of theoretical descriptions of mean field models of spin-glasses. A scaling theory is shown to describe the global and local fluctuations of the observables. We then investigate the effective temperature of jammed granular matter. The measurement of the effective temperature is realized in the laboratory by slowly shearing a closely-packed ensemble of spherical beads confined by an external pressure in a Couette geometry. All the probe particles, independent of their characteristic features and the shear rate, equilibrate at the same temperature, given by the packing density of the system. This suggests that the temperature reveals the ``thermalization'' of the jammed system. Finally, jammed emulsions are investigated under the confocal microscope. Owing to a new technique to identify the contact network in a 3D assembly of droplets, we reveal new signatures of jamming from micromechanics to statistical mechanics.   

Onset of jamming for gas-fluidized grains

Upon approach to jamming, whether for molecular liquids or colloidal particles or grains of sand, the microscopic dynamics can develop dramatic long-ranged correlations while the microscopic structure remains relatively unchanged. Experimentally, it has been difficult to study such phenomena in full detail due to the range of temporal and spatial scales involved. Here we introduce a new model system that is both easier to image and to manipulate at the microscale: a bidisperse system of steel beads rolling stochastically due to a nearly-levitating upflow of air. At fixed air flow, we demonstrate that this system exhibits all the hallmarks of a jamming transition as spheres are added and the area fraction increases toward close-packing. In terms of structure, the pair correlation function and the Voronoi cell shape distribution functions exhibit peak splitting. In terms of dynamics, the mean-squared displacement develops a plateau separating the short-time ballistic from the long-time diffusive motions; in this plateau the displacement distribution is non-Gaussian, due to spatial heterogeneities. While this phenomenology is familiar, one feature observed previously only in simulation is the presence of string-like swirls of rearranging grains. We highlight these by movies of an appropriately time-averaged velocity field. We hope to connect such dynamics both to a microscopic measure of effective temperature and to the macroscopic viscosity of the system.   

Force heterogeneity and stress propagation inside 3D granular materials

The effect of increasing structural disorder on the (re)distribution of contact stresses inside three dimensional particle assemblies is systematically studied using computer simulations of granular packings. Starting from a face-centred cubic array, where all contact forces are identical, particles are removed at random and the system is then allowed to relax into a new mechanically stable state. Various measures are used to quantify the amount of disorder, including distributions of the coordination number, three-particle contact angle, and normal contact forces. Upon applying a localised, perturbative force within the central region of the packings, the resulting stress response is mapped inside the different particle assemblies, covering several orders of magnitude in the particle friction coefficient. There is a clear change in the propagative response between frictionless and highly-frictional packings, with an intermediate, crossover regime for packings with lower values of the friction coefficient.   

Transitions from jammed to flowing granular matter

In static and slowly flowing granular materials forces are transmitted through a network of direct particle contacts. We experimentally examine how the contact networks fails and rearranges as granular matter starts to flow. Through surface measurements and 3D imaging of particle motion and forces we deduce how a granular contact network breaks and re-forms under shear forcing and point forcing. At small forcing, in the jammed state, we observe that low probability ``jumps,'' in which a grain moves significantly more relative to the others, play a significant role in the relaxation of the jammed state[1]. Under larger local forcing, the jammed state fails and grains rearrange locally. The characteristics of this rearrangement sensitively depend on the number density of particles and direction of forces that had been applied to jam the material (history dependence). If the direction of principal stress is changed (e.g. by changing the shear stress direction), the contact network breaks everywhere. The material is transiently weaker, more compact, and exhibits linear strain until a new contact network forms cooperatively[2]. [1] WL and M. Toiya with P. Ribiere, P. Richard, R. Delannay and D. Bideau to appear in Phys Rev. Lett. (2005). [2] M. Toiya, J. Stambaugh, and WL, Phys Rev Lett. 83, 088001-1 (2004).